Abstract: A system calculates the mutual satisfaction between negotiating parties and maximizes their mutual satisfaction over a range of decision variables and does so without requiring the parties to identify themselves and their positions to each other. For automatically negotiating agreements between multiple parties, a computer accepts a satisfaction function from an offering party who defines his degree of satisfaction to agree to a range of terms upon which the party is desirous of negotiating as a function of the relevant decision variables. The computer then accepts input from all other parties regarding their degree of satisfaction to agree to each of the terms as a function of a particular relevant decision variable. The computer then calculates a satisfaction function for each of these terms based on all of the individual inputs.